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A detector generally provides values that are proportional to the power spectral density (PSD) of the radiation hitting it. Energy per time interval (collection time), per spectral interval (pass band, slit width, pixel width, ...). The Fourier transform of the PSD is the time-domain autocorrelation function of the radiation. The autocorrelation function ...

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Presumably you have measured your spectrum as a function of wavelength, so you have $\mathscr{F}(\lambda)$, which is an power per unit wavelength. You must now convert this power per unit frequency spectrum. So we seek $\mathscr{G}(f)$ where $\mathscr{G}(f)\,|df| = \mathscr{F}(\lambda)\,|d\lambda|$; given $c = f\,\lambda$ we have: d\lambda = ...

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What kind of electronics do you have? Any photodiodes? What about a counter? You could use the two to improve your measurement of the Na wavelength by counting fringes electronically. Another variation on your ideas is to put a sealed glass cell into one of the arms and pump it with air to measure the index of refraction of air as a function of pressure. ...

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A very interesting question. It looks like you are right, with a light enough beam splitter and a photon with enough momentum the interference effects will vanish as the beam splitter "measures" the photons. Source: Quantum Processes Systems, and Information by B. Schumacher, et al. Section 10.4.

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